Corn alone, indeed any grain alone, is incomplete.
Ive done alot of research on this. Indeed, yesterdays "free-range" farm flock was a pretty dismal affair, by and large, just for the practices were discussing here.
There were some flocks that were well cared for, but they were the exception. Did you know that less than a hundred years ago, we lagged behind the entire world in poultry products.
Even the Aussies had us beat - by long mile!
Forage on a range varies. In the spring it's good, but as summer comes on it changes - the bugs get faster and the plants tougher. Chickens themselves quickly deplete what is there, with little regard for over foraging.
I've read that it takes an entire acre to provide for the needs of one chicken on a completely foraged diet.
Sure they did it in the old days, mostly since they didnt know any better. And quite likely because they had other animals beside poultry on the farm. The chickens could feed on the leftovers and droppings of these other endeavors. It took a lot of effort in those days to raise the level of America's poultry efforts to anything approaching what we take for granted today.
And we moderns, how we love the rustic notion of the free roaming flock taking care of itself, while it serves our needs. It takes us back to the "good old days." But what are/were the birds missing? What could have been done better?
If you really don't care beyond just having a few chickens around - then throw them some scratch and scraps and be done with it, by all means.
If you want to do better, however, I suggest you offer them a complete, all purpose ration. When the foraging is good, they will shun it. When things get slim out there on the range, they will head back to the feeders.
In the end they will be better fed and healthier - and you will reap the reward for that.